The aim of this talk is to introduce a coupled surface and subsurface flow problem arising from flood prediction and control. The mathematical and computational challenges are: (1) model deveoplement and model reduction, (2) numerical approximation for shallow water equation with complex physics, (3) algorithm design, (4) computer simulation/implementation, and (5) validation. The first four challenges shall be discussed in this talk, and particularly emphasis will be given to the model development and algorithm design. The talk should be accessible to general audience in applied/computational mathematics and hydraulogy.